📚 Year 7 WJEC Geography: Formula and Theorem Quick Reference Guide | Year 7 WJEC 地理：公式定理速查手册
This quick reference guide pulls together the essential formulas, calculations and data skills you will meet in Year 7 WJEC Geography. Having these tools at your fingertips will help you answer mapwork questions, analyse population data, interpret climate graphs and tackle fieldwork investigations with confidence. Each section explains what the formula does, shows you how to use it and gives a worked example where helpful.
本速查手册汇集了 Year 7 WJEC 地理课程中所需的基本公式、计算方法和数据技能。掌握这些工具能帮助你自信地解答地图题、分析人口数据、解读气候图以及完成野外实地调查。每一部分都说明了公式的用途、使用方法，并在适当的地方给出了计算示例。
1. Map Scale and Distance | 地图比例尺与距离
Map scale explains how many times the real world has been reduced to fit on a sheet of paper. On a WJEC map you will often see scales written as ratios, such as 1:25 000, or shown as a scale bar. The ratio means that one unit of length on the map stands for 25 000 of the same units on the ground.
地图比例尺表示真实世界被缩小了多少倍才能印在一张纸上。在 WJEC 地图中，比例尺通常以比数形式出现，例如 1:25 000，或者以图示比例尺的形式给出。这个比数意味着地图上一个单位的长度代表地面上的 25 000 个相同单位。
To convert a map distance into the real ground distance, multiply the measured length by the scale denominator. Always convert the answer into a sensible unit such as metres or kilometres.
要将图上距离转换为实际地面距离，只需用测量出的长度乘以比例尺分母。最后一定要把结果换算成一个合理的单位，比如米或千米。
Real Distance = Map Distance × Scale Factor
实际距离 = 图上距离 × 比例因子
Worked example: A footpath measures 6.5 cm on a 1:50 000 map.
Real distance = 6.5 cm × 50 000 = 325 000 cm = 3 250 m = 3.25 km.
计算示例：在 1:50 000 的地图上，一条步行小径的长度是 6.5 厘米。
实际距离 = 6.5 cm × 50 000 = 325 000 cm = 3 250 m = 3.25 km。
2. Calculating Area Using Grid Squares | 利用网格方格计算面积
Many WJEC map extracts include a grid of numbered lines. Once you know the area covered by one grid square, you can estimate the area of a feature such as a woodland, a lake or a housing estate by counting squares.
许多 WJEC 地图剖幅都带有编号网格线。当你知道了每个方格所代表的实际面积后，就可以通过数格子的方法来估算林地、湖泊或住宅区等地物的面积。
Area = Number of squares × Area of one square
面积 = 方格数量 × 每个方格的面积
Tip: When a feature does not fill a whole square, count parts that are more than half as one full square and ignore parts that are less than half. This is called the 'tick' or 'majority' method.
提示：当地物没有占满整个方格时，将超出半个方格的部分计为一个完整方格，不足半个的部分则舍去。这种方法称为“过半计数法”。
half-full squares, count as 7 + 3 = 10 squares, so the area is approximately 10 km².
示例：在一张 1:25 000 的地图上，网格边长为 4 cm，一个方格代表 1 km × 1 km = 1 km²;。假设一片森林覆盖了 7 个完整方格和 6 个半满方格，计数为 7 + 3 = 10 个方格，因此面积大约是 10 km²。
3. Gradient (Steepness of a Slope) | 坡度（斜坡的陡峭程度）
Gradient describes how steep a slope is. It is the ratio between the vertical rise (change in height) and the horizontal distance between two points. The formula is often written as a ratio of 1 to something, e.g. 1 : 10.
坡度用来描述斜坡的陡峭程度。它是两点之间的高差（垂直上升）与水平距离的比数。通常我们会将结果写成一个 1 比多少的比数，例如 1 : 10。
Gradient = Vertical Rise ÷ Horizontal Distance
坡度 = 垂直升高量 ÷ 水平距离
The rise and the horizontal distance must be in the same units (both in metres, for example). Find the rise by reading contour lines, and measure the map distance between the two points, then convert it to ground distance.
高差和水平距离必须使用相同的单位（例如都使用米）。高差可以通过读取等高线获得；水平距离则需先在地图上量出两点间的长度，再换算为实际地面距离。
. To express as a 1-in-__ ratio, divide both sides by 80: 80/80 = 1, 400/80 = 5, so 1 : 5.
计算示例：两地的实际水平相距 400 m，高度上升了 80 m。坡度 = 80 ÷ 400 = 0.2。要表示为 1 比 __ 的形式，可将两边同时除以 80：80/80 = 1，400/80 = 5，因此坡度为 1 : 5。
4. Population Density | 人口密度
Population density measures how crowded a place is. It is the average number of people living in each square kilometre of land. Geography students use it to compare settlements and regions.
人口密度衡量的是一个地方的拥挤程度。它表示每平方公里土地上平均居住的人口数量。地理学习者利用它来比较不同的聚落和区域。
Population Density = Total Population ÷ Area (km²)
人口密度 = 总人口数 ÷ 面积（km²）
dividing by 100 (since 1 km² = 100 ha). The result is written as people per km².
务必检查单位：若面积以公顷为单位，需要先除以 100 转换为 km²（因为 1 km² = 100 公顷）。结果的单位是“人/ km²”。
per km². This helps explain pressure on services such as schools and health centres.
案例分析：一个村庄有 2 400 位居民，占地 3 km²。人口密度 = 2 400 ÷ 3 = 800 人/ km²。这有助于解释学校和医疗中心等服务设施面临的压力。
5. Mean, Median and Mode for Geographical Data | 地理数据中的平均数、中位数和众数
When you collect fieldwork data, such as pebble sizes, river depths or traffic counts, you need to summarise your findings. The mean, median and mode are three ways to describe the 'average' or typical value.
当你收集到野外数据，如卵石大小、河流深度或交通流量时，需要概括你的发现。平均数、中位数和众数是描述“平均值”或典型值的三种方法。
Mean = Sum of all values ÷ Number of values
平均数 = 所有数值之和 ÷ 数值的个数
Median = Middle value when data are ordered
中位数 = 将数据按大小排列后处于中间位置的值
Mode = Most frequently occurring value
众数 = 出现频率最高的值
The mean uses every piece of data but can be pulled away by one extreme result. The median is not affected by outliers, so it is often used for skewed data like household income. The mode is useful for categorical data, for instance the most common land use in a survey.
平均数用到了所有数据，但容易被一个极端值拉偏。中位数不受异常值的影响，因此常用于偏斜的数据，如家庭收入。众数对类别数据很有用，比如在土地利用调查中出现最多的利用类型。
6. Percentage Change | 百分比变化
Geographers use percentage change to describe how a variable such as population, rainfall or tourism numbers has altered over time. It shows the relative increase or decrease compared with the original value.
地理学者用百分比变化来描述人口、降雨量或游客人数等变量随时间的变化程度。它显示了相对于原始数值的相对增加或减少。
rcentage Change = ((New Value − Original Value) ÷ Original Value) × 100
百分比变化 = （（新数值 − 原始数值） ÷ 原始数值） × 100
A positive answer means an increase; a negative answer shows a decrease. Always state which period the change covers, and round your answer to one decimal place unless told otherwise.
若计算结果为正，表示增加；为负则表示减少。务必说明变化所覆盖的时间段，除非题目另有要求，一般将结果四舍五入至一位小数。
Example: A town' − 12 500) ÷ 12 500) × 100 = (1 300 ÷ 12 500) × 100 = 10.4% increase.
示例：一个城镇的人口从 12 500 增长到 13 800。变化 = （（13 800 − 12 500） ÷ 12 500） × 100 = （1 300 ÷ 12 500） × 100 = 10.4% 增长。
7. Compass Directions and Bearings | 罗盘方向和方位角
Accurate direction is a core map skill. WJEC questions frequently ask you to give the compass direction from one place to another, or to measure a precise bearing using a protractor.
准确辨别方向是一项核心的地图技能。WJEC 考题经常要求你给出从一个地点到另一个地点的罗盘方向，或者用量角器测量出一个精确的方位角。
The eight and sixteen compass points give approximate directions (e.g. north-east, south-south-west). For a precise angle, bearings are measured clockwise from true north and written as a three-digit value between 000° and 360°.
八方位和十六方位罗盘给出的是近似方向（如东北、西南偏南）。要得到精确的角度，方位角是从正北起按顺时针方向测量的，记录为一个介于 000° 到 360° 之间的三位数。
To measure a bearing: place the centre of the protractor over the starting point, align 0° with north on the map, and read the angle to the line joining the two points.
测量方位角的方法：将量角器的中心点对准起点，使 0° 刻线与地图正北方向对齐，然后读取起点与终点连线的角度读数。
8. Climate Averages and Totals | 气候平均值和总量
Climate graphs are a combination of a line graph for temperature and a bar chart for rainfall. To construct or read them, you need to be able to calculate simple averages and totals.
气候图是用于表现气温的折线图和用于表现降雨量的柱状图的结合体。无论是绘制还是判读气候图，你都需要会计算简单的平均值和总量。
Average Temperature = Sum of temperatures ÷ Number of readings
平均气温 = 气温读数总和 ÷ 读数个数
Total Annual Precipitation = Sum of all monthly rainfall
年总降水量 = 各月降雨量之和
When dealing with temperature range, subtract the coldest month's average from the warmest month's average. This figure helps describe how extreme a climate is.
计算气温年较差时，用最热月的平均气温减去最冷月的平均气温。这个数值有助于描述气候的极端程度。
, 4°C. Sum = 130°C. Mean annual temperature = 130 ÷ 12 ≈ 10.8°C.
示例：各月气温 ;C, 10°C, 14°C, 17°C, 19°C, 19°C, 15°C, 11°C, 7°C, 4°C。总和为 130°C。年平均气温 = 130 ÷ 12 ≈ 10.8°C。
9. Vertical Exaggeration on Cross-Sections | 地形剖面图中的垂直夸大
When you draw a cross-section from a contour map, the vertical scale is often made larger than the horizontal scale to make the shape of the land clearer. Vertical exaggeration tells you how many times the height has been stretched compared with the width.
在根据等高线地图绘制地形剖面图时，为了让地表形态更加明显，垂直比例尺通常会比水平比例尺大。垂直夸大表示的是剖面图中的高度相对于宽度被放大了多少倍。
Vertical Exaggeration = Vertical Scale ÷ Horizontal Scale
垂直夸大 = 垂直比例尺 ÷ 水平比例尺
00 and the vertical scale is 1:10 000, then VE = (1/10 000) ÷ (1/50 000) = 5 times.
在进行除法运算前，两个比例尺必须表示成分数或比数，并且单位相同。如果水平比例尺为 1:50 000，垂直比例尺为 1:10 000，那么垂直夸大 = （1/10 000） ÷ （1/50 000） = 5 倍。
A vertical exaggeration of between 2 and 5 is typical for school cross-sections. Too much exaggeration distorts the slope angles, so always check your choice.
学校常用的地形剖面图垂直夸大多在 2 到 5 倍之间。过分夸大会使坡角变形失真，所以要时常检验你的选择。
10. River Discharge (Basic Introduction) | 河流流量（基础入门）
River discharge is the volume of water passing a point in a river every second. It is a key measurement in flood studies and helps geographers understand how much energy a river has to erode, transport and deposit material.
河流流量是指每秒钟流经河道某一点的水的体积。它是洪水研究中的一项关键测量数据，有助于地理学者理解河流拥有多少能量来进行侵蚀、搬运和堆积物质。
Discharge (m³/s) = Cross-sectional area (m²) × Velocity (m/s)
流量（m³/s） = 河流横截面积（m²） × 流速（m/s）
In Year 7 you may not be required to calculate discharge from measurements, but understanding this relationship helps you explain why a river's speed and power increase as it moves downstream. A wider and deeper channel plus faster-moving water combine to give a much larger discharge.
在 Year 7，你可能不需要从实测数据开始计算流量，但理解这个关系能帮助你解释为什么河流越往下游流速和动力越大。更宽更深的河道加上更快的水流，共同造成了更大的流量。
Fieldwork connection: If you measure width, depth and velocity during a river study, you can find the cross-sectional area by multiplying average depth by width, then multiply by velocity to estimate discharge.
野外实地联系：在河流考察中测量了宽度、深度和流速后，你可以用平均深度乘以宽度得到过水断面面积，再乘以流速来估算流量。
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